How would you define the shape? If you use mathematical equations then you can integrate the shape.
2006-12-20 16:16:32
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answer #1
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answered by rscanner 6
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it extremely is exciting because of the fact classic solids like spheres and cubes or maybe cones won't be able to share the comparable volumes and surfaces. to illustrate, if it have been achievable to discover a cone that has the comparable quantity and floor as a sphere, then it does not be actual that the sector might have the minimal floor for a given quantity. enable me think of roughly this for a whilst. i'm advantageous that looking 2 solids, the two considered one of which demands no less than 2 variables to describe, alongside with a cylinder and a cone, of having the comparable quantity and floor isn't probably a concern. Edit: is that this concern constrained to "classic" generally going on figures that have in simple terms one scaling variable? Edit 2: Oh, wow, thank you for clearing up that mistake. i became approximately waiting to instruct that a answer is impossible for any sturdy it extremely is defined by a single scaling variable. ok, enable me get returned to that. Edit 3: i'm not probably attracted to trivial suggestions alongside with a cuboid with top h = 2.0228358440627425 and factors w = w = 7.1323556324725805, which might have the comparable quantity and floor section as given. i visit make sure if i will come across a "single scaling variable" sturdy that meets the circumstances. i comprehend that it extremely is not "prima facie impossible", now which you have have been given given the main appropriate floor section. Edit 4: properly, that became ordinary, my first try. The polyhedron you're finding at is a tetrahedron. It has a "function" of 0.05170026995011663 that's extremely on the verge of crumple of the function of your secret "polyhedron". It has a area length of 9.594752190203167. it would possibly be observed that a single scaling variable sturdy that has a function cost won't be able to ever have the comparable quantity and section as yet another single scaling variable sturdy with a different function. Of each and all the only scaling variable solids, the sector has the utmost achievable cost for the function, that's 0.09403159725795937. Edit 5: for human beings that choose a proof of what's a function of a sturdy, if a sturdy's quantity and floor section is given as Ax³ and Bx², the place x is any variable alongside with area length or radius, then the function is A/(B)^3/2. for this reason, the scaling component drops out of the photograph. Edit 6: because of the fact the sector has the optimal "function", you may invent virtually the different function by getting some style of a hollow area in the sector.
2016-12-30 15:33:07
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answer #2
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answered by Anonymous
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